Problem started with engine cutting out after 5 min mowing. Restart difficult, but soon found push/pull of ignition key did the trick. Once running, could stall it by nudging key "wrong way." Assumed need to replace ignition switch or loose wire in connector, etc. Yesterday, started engine, but died after 10 seconds or so. Now will not start or even fire. Solenoid, starter, fuse, gas all ok. Pulled & opened up ignition switch: Looks worn, but not sure what it is supposed to look like inside. Which terminals to jumper to check if ignition switch bad? Plug newish, but will replace tomorrow. Need ideas/troubleshooting sequence. Have multimeter, 12V tester, and experienced brain.
Thanks folks! All done. Well, almost: I replaced the spark plug and ignition unit, put it back together and spent the next 3 hours cutting grass. Fired up like brand new. I had to order the ignition switch online, so will take 2 minutes swapping it out next week. Cheap insurance to prevent another occurrence.
FYI - The ignition coil is called "ignition unit" on this engine and I could not find it listed on searspartsdirect.com. This drove me crazy, until (head slap here) I went to the Kohler website, found the part number, located a nearby dealer, and picked it up after a 10 minute drive. It was about $55 compared to $31 online, but I got it today before I lost another cat to the encroaching yard jungle.
